y=5y^2+(y-5)

Solution for y=5y^2+(y-5) equation:

y=5y^2+(y-5)

We move all terms to the left:

y-(5y^2+(y-5))=0


We calculate terms in parentheses: -(5y^2+(y-5)), so:

5y^2+(y-5)

We get rid of parentheses

5y^2+y-5

Back to the equation:

-(5y^2+y-5)


We get rid of parentheses

-5y^2+y-y+5=0

We add all the numbers together, and all the variables

-5y^2+5=0

a = -5; b = 0; c = +5;
Δ = b2-4ac
Δ = 02-4·(-5)·5
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10}{2*-5}=\frac{-10}{-10}
=1
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10}{2*-5}=\frac{10}{-10}
=-1
$